Figure REF  shows a real world scenario on the left.
Infering an interaction potential from that scene is difficult.
On the right side of this figure, I share the result of a first attempt.
The MLP is initialized with a fit to synthetic
data and then fine-tuned on the real world example
from the “Crowd by Example” dataset [1]}
as provided in the TrajNet++ challenge [2]}.
The optimization does not converge and does not work without the initialization
from synthetic data.
If one wanted to force an interpretation of this result, one would highlight the
two distinct regimes
below and above \(b=1\,\textrm {m}\) . For \(b < 1\,\textrm {m}\) , the potential is
repulsive as in the classical Social Force model. For \(b > 1\,\textrm {m}\) ,
the potential is attractive. This type of behavior would have been impossible
to discover with a functional constraint to a falling exponential as in the
classical Social Force model [3]}. The reason for the
attractive nature of the potential is likely due to the large number of
social groups (groups of friends or classmates) in this dataset.
The classical Social Force
model actually does have a separate interaction term for the attractive forces
but here this behavior is discovered from data.
